(1) Selective Magnetic Dilution and Site PercolationThe selective magnetic dilution has been studied by the new effective field theory (NEFT) on the lattices with several kinds of two-sublattice structures. Sublattices A and B are assumed to be randomly but selectively diluted by non magnetic atoms, keeping dilution ratio U=(1-p_B)/(1-p_A) constant, and the global phase diagrams of T_C(p_A, p_B) has been calculated. In conjunction with the phase diagram at T=OK,we investigated selective site percolation of this system by real space renormalization group theory and clarified the role of site selectivity U in the study of thecorrelation length exponent and the fractal dimension of the incipient percolation cluster.(2) An Effective Field Theory for Dilute Anisotropic Heisenberg FerromagnetsDilute anisotropic Heisenberg ferromagnets have been studied by NEFT based on a two-site cluster approximation with an Ising character assumed for the surrounding spins. The results for the Curie temper
… Moreature, T_C, and the critical concentration for magnetic ordering are improvements on those of a single-site approximation where the exchange anisotropy cannot be accounted for. The initial reduction in T_C with dilution has been confirmed to decrease with increase in both the lattice coordination number and exchange anisotropy.(3) Bilinear-Biquadratic Quantum Exchange Model with Single-Ion Uniaxial AnisotropyThe above calculation has been extended to the system of spin S=1, including biquadratic exchange interaction J' and single ion anisotropy D.In particular, we studied the cross-over from anisotropic Ising to isotropic Heisenberg behavior in the variation of T_C with strength J', and also discussed about a spurious reentrant transition phenomena which is found in the vicnity of the critical concentration over a range of strength D.For the isotropic case of D=0, we showed rigorously that the ground state of the Hamiltonian is always singlet on a connected finite lattice with an even number of site, if the exchange interactions satisfy the condition J'>J>0.なお、選択的磁気希釈に対する実空間繰り込み群の開発の課題については現在研究を進行中である。 Less